A general upper bound on the size of constant-weight conflict-avoiding codes

Authors:
Kenneth W. Shum;Wing Shing Wong;Chung Shue Chen
Affiliations:
Department of Information Engineering, The Chinese University of Hong Kong, Shatin, Hong Kong;Research Group on Network Theory and Communications, INRIA-ENS, Paris, France;Research Group on Network Theory and Communications, INRIA-ENS, Paris, France
Venue:
IEEE Transactions on Information Theory
Year:
2010

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Abstract

Conflict-avoiding codes are used in the multiple-access collision channel without feedback. The number of codewords in a conflict-avoiding code is the number of potential users that can be supported in the system. In this paper, a new upper bound on the size of constant-weight conflict-avoiding codes is proved. This upper bound is general in the sense that it is applicable to all code lengths and all Hamming weights. Several existing constructions for conflict-avoiding codes, which are known to be optimal for Hamming weights equal to four and five, are shown to be optimal for all Hamming weights in general.